Analytic explanation of the effective-temperature coincidence

Determine analytically why the effective temperature at the current-driven tricritical point in the D3/D7 holographic nonequilibrium steady state nearly coincides with the heat-bath temperature, yielding T*/T approximately equal to 0.9998.

Background

The paper numerically finds that the effective temperature associated with the open-string-metric horizon is almost equal to the heat-bath temperature at the current-driven tricritical point. Because the effective temperature depends nontrivially on the external electric and magnetic fields and on the background D7-brane configuration, the observed near-coincidence is not explained by the numerical analysis. Establishing an analytic explanation would clarify the origin of this feature of the tricritical point.

References

We have not been able to explain this coincidence analytically because the effective temperature is a complicated function of the external fields and the D7-brane configuration, and the TCP lies in a highly nonlinear region.

— Landau theory, effective temperature, and tricritical phenomena in a holographic nonequilibrium steady state  (2608.23378 - Kanazawa et al., 24 Aug 2026) in Section 5, Conclusions and discussion